Variables and Measurement (2.1) Variable - Characteristic that takes on varying levels among subjects Qualitative - Levels are unordered categories (referred to as nominal scale) Quantitative - Levels vary in magnitude (referred to as interval scale) Combination - Levels are ordered categories (referred to as ordinal scale)

Statistical Methods (2.1) Statistical methods apply to the various variable types When conducting research it is important to identify what variable type(s) are being observed so that proper methods are used to describe the data and make inferences Ordering of variable types from highest to lowest level of “magnitude differentiation”: interval > ordinal > nominal

Interval Scale Variables (2.1) Discrete - Variable can take on only a finite (or countably finite) set of levels Continuous - Variable can take on any values along a continuum Discrete variables with many possible outcomes are often analyzed as if continuous Continuous variables often reported as if discrete

Randomization Quality of inferences depends on how well a sample is representative of a population Simple Random Sampling: All possible samples of n items from a population of N items are equally likely. Makes use of random number tables or statistical software that can quickly generate long lists of random numbers. Frame (or listing) of all items in population must exist to truly implement simple random sampling

Probability & Non-Probability Samples Probability Samples: Probability of given samples being selected can be computed. Non-probability Samples: Probability of possible samples cannot be specified: Volunteer samples: Mail-in questionnaires, internet click on responses, Call-in surveys Street corner surveys Inferential methods valid only for probability samples

Experimental Designs Experimental Studies: Researcher assigns subjects to experimental conditions. Subjects should be assigned at random to the conditions, and preferably blinded to the specific treatment when possible (e.g. Clinical trials) Randomization in long trials will “balance” treatment groups with respect to other demographic risk factors Sample surveys that identify subjects by naturally occurring groups are Observational

Sampling & Non-sampling Variation Sampling Error: Difference between a statistic computed on a sample and the true population parameter. Typically unknown except in academic examples Methods exist to predict magnitudes (margin of error) Non-sampling Error sources: Undercoverage: Frame may not contain all individuals of certain groups (e.g. telephone books) Nonresponse: Individuals who complete surveys may differ from those who don’t Response Bias: Taboo questions / “Politically correct” answers

Probability Sampling Methods Alternatives to Simple Random Sampling (need adjustments to some formulas): Systematic Random Sample: Choose an item at random at top of frame, then select every kth item Stratified Random Sample: Identify groups of individuals by some characteristic (strata), and take simple random samples within each strata. Cluster Sample: Identify individuals by clusters (typically locations) and randomly sample clusters of individuals.